The invention relates to double-ended tuning forks and particularly to double-ended tuning forks as used in the construction of accelerometer devices and the cancellation of second order non-linearity thereof.
Non-linearity in accelerometer outputs can lead to significant measurement errors in the absence of compensation circuitry. Generally, non-linearity errors occur when inputs are near the full-scale range of the instrument or there is vibration along the input axis, but non-linearity errors may also appear simply because the particular application requires an extremely linear response. Instruments using double-ended tuning forks, or DETFs, as inertial reaction force sensors are particularly vulnerable to errors introduced by non-linearity. The inherent non-linearity of a force sensor or accelerometer using a single DETF is typically higher than that of a common high-accuracy, analog, force-rebalance accelerometer, as described in U.S. Pat. Nos. 3,702,073 and 4,250,757, for example.
A DETF-based accelerometer, however, possesses real advantages over other accelerometers. For example, a DETF-based accelerometer typically provides smaller size, lower power consumption, and greater ease of interface to digital systems. Compensation of DETF-based accelerometer non-linearity provides all these benefits without a serious performance penalty.
Practical accelerometers in the past have used software compensation of non-linearity, or a combination of software and hardware compensation. Software compensation is not viable for other than constant or slowly varying acceleration inputs because the processor cannot execute the compensation commands at frequencies high enough to keep pace with the accelerometer inputs.
One combined software and hardware compensation approach that has been used is to infer the input acceleration based on models that depend on the difference frequency between two DETFs. This approach assumes that the DETFs have been designed to possess the same second-order non-linearity when subjected to purely axial forces.
The DETFs may be attached either to one or to two independent proof masses. Dual-proof mass accelerometers are really two separate accelerometers in the same package. Using dual-proof mass accelerometers leads to difficult matching problems to ensure that the responses of the two accelerometers track when the accelerometer experiences vibration or other rapidly-changing inputs.
A common approach to avoiding the common mode tracking problems created by using two accelerometers in one package is to attach two DETFs to a single proof mass, arranging them so that displacement of the proof mass under loading simultaneously places one of them in tension and the other in compression. In practical accelerometers, the exact arrangement of the DETFs is dictated by several factors. One factor is the need to incorporate stress isolation, for example, see U.S. Pat. No. 4,766,768, the complete disclosure of which is incorporated herein by reference. Another factor is the necessity of having both DETFs on the same side of the proof mass in monolithic silicon accelerometers built with epitaxial layer DETFs. Other reasons which do not consider the effect of the DETF positions on the non-linearity of the accelerometer such as manufacturing tolerances or other processing limitations, or size restrictions also dictate the exact arrangement of the DETFs.
General information on the design of vibrating beam accelerometers may be found in the text by Lawrence entitled Modem Inertial Technology: Navigation, Guidance and Control, Copyright 1993, Springer-Verlag, New York.
FIG. 1 shows a plan view of a DETF accelerometer which combines a proof mass 2 and DETFs 4, 6. DETFs 4, 6, however, are positioned at much different distances 14, 16 from the centerline 8 of the hinges 10, 12 suspending proof mass 2. Thus, the respective non-linearity of the two DETFs do not cancel effectively when the difference frequency is formed, even when the DETFs are designed for the ideal case in which second-order non-linearity, K2, values cancel when subjected to purely axial forces. The lack of second-order non-linearity cancellation when the difference frequency is formed causes measurement errors and creates difficulties when DETF force sensors and accelerometers are used in applications requiring a high degree of linearity.
Above incorporated co-pending parent U.S. patent application Ser. No. 08/873,048 describes a method for determining relative positioning of the DETFs in a dual vibrating beam accelerometer which substantially overcome the problems of the prior art by providing positioning of the two DETFs which minimizes or substantially eliminates second-order, K2, non-linearity effects. The parent application also provides various physical embodiments which place the two DETFs such that the individual DETF second-order values are a minimum and the composite second-order values are a minimum and the composite second-order terms cancel or substantially cancel.
However, as ever greater degrees of linearity are required by more and more sensitive accelerometer applications, additional fine tuning of second-order, K2, non-linearity effects is required to ensure complete or substantially complete cancellation of the composite second-order terms of two DETFs in a practical dual vibrating beam accelerometer.
The present invention overcomes the limitations of the prior art by recognizing and accounting for the deformation of the DETFs in a two-DETF, single-proof-mass accelerometer that are not purely axial extensions or compressions, but also involve rotations and transverse displacements of the ends of the DETFs. The rotations and displacements create additional changes in the tine stiffness, beyond those that occur due to simple stress stiffening effects. The additional stiffness changes alter the linearity of the DETFs so that the second-order effects such as those due to, for example, Euler buckling loads, do not cancel when the difference frequency is formed.
According to one aspect of the present invention, the present invention includes various embodiments which overcome the limitations of the prior art by providing mass balances positioned on each of the two DETFs which minimize or eliminate second-order, K2, non-linearity effects.
According to another aspect of the present invention, the invention provides a double-ended tuning fork (DETF) sensor having first and second DETFs, a proof mass, a support frame, and a hinge rotatably suspending the proof mass from the support frame. The two DETFs are spaced apart and connected between the proof mass and the support frame. The first and second DETFs are each constructed having two tines. According to the invention, mass balances are formed projecting from each of the tines of the first DETF and are sized and positioned to form a first second-order non-linearity term associated with the first DETF. Similarly, mass balances projecting from each of the tines of the second DETF are sized and positioned to form a second second-order non-linearity term associated with the second DETF such that the second second-order non-linearity term is substantially equal in sign and magnitude to the first second-order non-linearity term.
According to one aspect of the invention, the proof mass and support frame are formed in a silicon wafer having an active epitaxial layer formed on one surface thereof, and each of the DETFs and the mass balances are formed in the active epitaxial layer.
According to another aspect of the invention, the mass balances project outwardly from the edges of the tines in a formation substantially symmetrical about a longitudinal axis of the respective DETF. In particular, the mass balances are formed along an edge of each tine as a function of the second-order non-linearity term associated with the respective DETF, such that the mass balances adjusts the second second-order non-linearity term associated with each DETF to a value substantially equal in magnitude to the second-order non-linearity term associated with the other DETF.
According to still another aspect of the invention, the multiple mass balances project from each of the tines.
According to another aspect of the present invention, the invention provides methods for sizing and positioning the mass balances on one or both of the dual-DETFs such that second-order non-linearity of the two DETFs are equal or substantially equal under the deformations that they actually undergo in use. Thus, the present invention provides cancellation of the composite second-order non-linearity.